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n^2+84n=9
We move all terms to the left:
n^2+84n-(9)=0
a = 1; b = 84; c = -9;
Δ = b2-4ac
Δ = 842-4·1·(-9)
Δ = 7092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7092}=\sqrt{36*197}=\sqrt{36}*\sqrt{197}=6\sqrt{197}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-6\sqrt{197}}{2*1}=\frac{-84-6\sqrt{197}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+6\sqrt{197}}{2*1}=\frac{-84+6\sqrt{197}}{2} $
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